On p-biharmonic equations with critical growth.

Abstract

We study p-biharmonic problems dealing with concave-convex nonlinearitiesin the critical case with both Navier and Dirichlet boundary conditions in a bounded, smooth domain and some f ε C(Ω), which is either a positive or a change-sign function. By applying Nehari’s minimization method, we prove the existence of two nontrivial solutions for the problems. If f is positive, both solutions of the problem with Navier boundary condition are positive.